The Censored Normal Distribution
Description
Density, distribution function, quantile function, and random generation for the left and/or right censored normal distribution.
Usage
dcnorm(x, mean = 0, sd = 1, left = -Inf, right = Inf, log = FALSE)
pcnorm(q, mean = 0, sd = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
qcnorm(p, mean = 0, sd = 1, left = -Inf, right = Inf,
lower.tail = TRUE, log.p = FALSE)
rcnorm(n, mean = 0, sd = 1, left = -Inf, right = Inf)
Arguments
x , q
|
vector of quantiles. |
p
|
vector of probabilities. |
n
|
number of observations. If length(n) > 1 , the length is taken to be the number required.
|
mean
|
vector of means. |
sd
|
vector of standard deviations. |
left
|
left censoring point. |
right
|
right censoring point. |
log , log.p
|
logical; if TRUE, probabilities p are given as log(p). |
lower.tail
|
logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x]. |
Details
If mean
or sd
are not specified they assume the default values of 0
and 1
, respectively. left
and right
have the defaults -Inf
and Inf
respectively.
The censored normal distribution has density \(f(x)\):
\(\Phi((left - \mu)/\sigma)\) | if \(x \le left\) |
\(1 - \Phi((right - \mu)/\sigma)\) | if \(x \ge right\) |
\(\phi((x - \mu)/\sigma)/\sigma\) | if \(left < x < right\) |
where \(\Phi\) and \(\phi\) are the cumulative distribution function and probability density function of the standard normal distribution respectively, \(\mu\) is the mean of the distribution, and \(\sigma\) the standard deviation.
Value
dcnorm
gives the density, pcnorm
gives the distribution function, qcnorm
gives the quantile function, and rcnorm
generates random deviates.
See Also
dnorm